intonation (n) - the rise and fall of the voice in speaking,especially as this affects the meaning of what is being said.

And,

accent (n) - a way of pronouncing the words of a language that shows which country, area or social class a person comes from.

Now, when an American has a way of pronouncing something, they do have rise and fall of the voice in speaking, don't they?

Having said this, if in AmE it is...

"I gat (got) to do it beybe (babe)" -pardon my making of onomatopoeia here. I'm not a native speaker.

And in InE it is...

I goat (got) to do it bebe (babe) - this is very close to how we utter it! Trust me!

Does AmE here differ in accent or intonation? If both, what's the nuance to understand for a person like me? If I don't understand something from an American movie or soap, is it an accent or intonation?

I guess accent in such case refers to one word whereas intonation is the entire sentence/conversation. Am I right? If I am, other way round --intonation can be applied to a word and accent could be of the whole sentence. If I say intonation, does it include accent or it's other way round? If I talk about accent, it includes intonation?

I think the word you're looking for here is "accent". All varieties of English have similar intonation, I think. Intonation is more like what words you place the stress on, or whether your sentence is a question or a statement. "This is yours." and "This is yours?" are not said the exact same way in verbal speech. There is an elongation of "yours" and a rise in pitch when it is asked as a question. That is intonation.
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AdmiralAdamaApr 22 '14 at 9:03

2 Answers
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Intonation is a general term for the pitch of your voice rising and falling as you speak:

It includes things like the pitch of your voice rising at the end of the sentence to signal a question, or lowered pitch to indicate a parenthetical phrase.

It excludes phonemic pitch contrasts used to distinguish words as in tonal languages (Thai, Mandarin) or pitch accent languages (Japanese)—although you might find some definitions that include this sort of thing.

Accent has a few different meanings. The relevant meaning here is "features of pronunciation that signal regional or social identity" (Cambridge Encyclopedia of Language, p.420). This could include differences in intonation between different groups of speakers, although I wouldn't go so far as to say it includes intonation generally.

Your examples of eye dialect appear to describe differences in vowels between different groups of speakers. This sort of difference falls under accent.

Dialect, by the way, is different from accent. It's defined as "a language variety in which the use of grammar and vocabulary identifies the regional or social background of the user" (Cambridge Encyclopedia of Language, p.425). So a word like prepone existing in Indian English but not American English is a matter of dialect rather than accent.

It's worth noting that your examples center on differences in pronunciation for two words: got and babe. Even in the U.S., you will find differences in how words like that are pronounced, and we refer to those as regional accents.

In the U.S., there is (this is not meant to be an exhaustive list):

The northeast (or Bostonian) accent, characterized by the way they pronounce (or some would say, don't pronounce) trailing r's. The classic test for this accent is: Go park the car in the yard. If you want to hear it, have a listen to Billy Baker on YouTube.

The upper Midwestern (or Minnesota/Wisconsin) accent, characterized an slightly elongated long o sound. Do you know how to row a boat? (For more examples, you can watch Fargo.)

The Southern accent, which is hard to describe in a sentence or two, but you can read more about it on Wikipedia, or hear samples on YouTube. I have a coworker from Tennessee, and I'm reminded of his origins every time he asks for a pen, because it sounds like he's asking for a pin.

In short, just like you can often tell if a speaker hails from the U.S., the U.K., Canada, Australia, or India just by a speaker's accent (yes, accent is the word you're looking for), you can also sometimes tell what region of the U.S. a speaker is from.

Some people keep their accent all their lives; for others, it will change based on where they currently live. I'm originally from the northeastern U.S., and my first job moved me to the Nebraska, which is in the dead center of the continental U.S. I went home on vacation, and was talking to an old friend of mine. All of a sudden, he started laughing, even though I wasn't saying anything funny.

"What are you laughing at?" I asked.
"You have an accent now!" he answered.
I replied, "Well, either I got one, or I lost one – it depends on your point of view!"

If you're interested in this kind of thing, you might enjoy a visit to Forvo.com, where speakers from all of the world pronounce words one at a time, sometimes with surprising variations. Root beer, anyone? Yeah, baby!

The United States does not have a concrete 'standard' accent in the same way that Britain has Received Pronunciation. Nonetheless, a form of speech known to linguists as General American is perceived by most Americans to be "accent-less", meaning a person who speaks in such a manner does not appear to be from anywhere. The region of the United States that most resembles this is the central Midwest, specifically eastern Nebraska (including Omaha and Lincoln), southern and central Iowa (including Des Moines), parts of Missouri, Ohio and western Illinois (including Peoria and the Quad Cities, but not the Chicago area).